Is there a place where people can share (or buy) ready made neural networks?
It's not a specific web for sell or share neural network models, but actually you can easily find other people models in Github! Just search it! For example, this is a random repo I've found for Cat Classification.
But.. the problem is everyone have different problems. So you can't easily use other people neural network models and then use it for your problem. That's why there's a &quot;trick&quot; called transfer learning or fine tuning. That method show you how to train other people models (it's called: pre-trained models) from different problems for your specific problem.
Tensorflow and PyTorch provide a lot of pre-trained model for common problems:

Pytorch Image Classification Pre-Trained models
Tensorflow Object Detection Model Zoo
PyTorch Detectron Model Zoo

You can also find other pre-trained models in Github! This is an official PyTorch tutorial how to use that pre-trained model to your specific case.